By now, wireless communication systems have been developed rapidly. The traditional second-generation mobile communication system, i.e. Global System for Mobile Communication (GSM), is continuously evolving toward General Packet Radio Service (GPRS) and Enhanced Data Rates for GSM Evolution (EDGE), to greatly improve data transmission capacity of the system. The third-generation mobile communication system with a higher transmission rate, such as Wideband Code Division Multiple Access (WCDMA) and CDMA2000, has been deployed in many countries and regions worldwide for starting to be put into commercial use. During the development of cellular communication technology, other wireless access technologies, such as Wireless LAN (WLAN) and Worldwide Interoperability for Microwave Access (WiMAX) technology, have been developed rapidly. In addition, an IEEE 802.16m technology facing the fourth-generation mobile communication system, a Third-Generation Partnership Project Long Term Evolution (3GPP LTE) technology and a Third-Generation Partnership Project Long Term Evolution-Advanced (3GPP LTE-Advanced) technology have entered into a research and development stage.
A multi-antenna system for MIMO (Multi-input Multi-output) can offer large increases in throughput due to its ability to support parallel data stream transmission, and draws more and more attention in academic researches and practical systems. Generally, in multi-antenna transmission, the parallel data streams are suffered to coding with forward error correction codes separately, and then the coded code words are mapped onto one or more transmission layers. To map the coded words onto multiple transmission layers, the serial data output from a coder are converted into parallel data on the respective layers. The number of all layers supported by the system in one transmission is also referred to as a rank (Rank) of the system.
Generally, the number of the transmission layers or the rank supported by the multi-antenna system is less than or equal to the number of physical antennas of the multi-antenna system. The process for transforming the data on the layers into data on the physical antennas is called as “pre-encoding” of a signal. In particular, the process for transforming the data on the layers into the data on the physical antennas by a linear operation is called as “linear pre-encoding” of the signal. In the existing wireless communication systems such as an LTE system and a WiMax system, it is needed to design a certain number of precoding matrices in advance for the system due to limitations in computational complexity and signaling control complexity of the system. A set of precoding matrices is called as a precoding matrix codebook, and the number of the precoding matrices in the precoding matrix codebook is called as the size of the precoding matrix codebook. In a multi-antenna system, the performance index of the system, such as throughput, is influenced directly by the precoding matrix codebook as well as the size of the precoding matrix codebook and the elements of the codebook precoding matrix book. Therefore, in order to maximize the throughput of the system, it is necessary to design the precoding matrix codebook of the multi-antenna system, including the size of the precoding matrix codebook and the precoding matrix elements of the precoding matrix codebook.